Positivity of lyapunov exponents for a continuous matrix-valued anderson model

We study a continuous matrix-valued Anderson-type model. Both leading Lyapunov exponents of this model are proved to be positive and distinct for all energies in ( 2,+ infinity) except those in a discrete set, which leads to absence of absolutely continuous spectrum in ( 2,+ infinity). This result is an improvement of a previous result with Stolz. The methods, based upon a result by Breuillard and Gelander on dense subgroups in semisimple Lie groups, and a criterion by Goldsheid and Margulis, allow for singular Bernoulli distributions.